Electric-field-induced modulation of the magnetic penetration depth of superconducting La$_{2-x}$Sr$_{x}$CuO$_{4}$ ultrathin films

A study of the electric-field-induced change of the in-plane magnetic penetration depth $\lambda _{ab}$ of an underdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO) ultrathin superconducting (S) film is reported for the first time. Using MBE, a two unit-cell (UC) thick (x$\approx $0.1) LSCO S-film was grown epitaxially on a 12 UC thick normal (x=0.4) LSCO buffer layer deposited on a monocrystalline. SrLaAlO$_{4}$ substrate. A capacitor structure was then patterned after growing on top of the S-film a 15 nm thick HfO$_{2}$ insulating layer with a dielectric constant $\varepsilon \approx $15 and a Pt gate electrode. The inverse kinetic inductance 1/L$_{k}\propto $ 1/$\lambda _{ab}^{2}$ of the LSCO film was measured using an inductive two-coil technique. Both the temperature (T) and magnetic-field dependences of 1/L$_{k}$ were investigated by applying gate voltages corresponding to electric fields E = $\pm $ (2 x 10$^{8})$ V/m. For the largest E-field modulation ($\Delta $E $\equiv $ 4 x 10$^{8}$ V/m) a relative change $\Delta $L$_{k}^{-1}$/L$_{k}^{-1}\approx $ 18{\%} was observed at low temperature in good agreement with an elementary theoretical estimate. The nonmonotonic T-dependence of $\Delta $L$_{k}^{-1}$/L$_{k}^{-1}$ (a maximum is observed where L$_{k}^{-1}$(T) has the largest slope) can be accurately described by a simple model assuming that L$_{k}^{-1}$(0) $\propto $ T$_{c}$.